A Program on Solidification and Fast Algorithms

凝固工艺在现代技术中无处不在。当一种物质从液体或气体变为固体时，例如冰融化或冻结时，当用于半导体器件的硅或砷化镓晶体生长时，或用于电影制作的卤化银晶体生长时，当阿拉斯加土壤的冻结模式被石油管道改变时，或者当锌枝刺穿铅锌电池的壁时。本活动的主题是凝固过程的计算机模拟，它有两个目的。在研究基础物理学时，任何提出的模型的理论预测都必须产生，并与其他模型和实验进行比较。凝固过程非常复杂，必须通过精确的数值模拟来完成；精确的解几乎不存在。一旦基本物理学被很好地理解了，数值计算就可以产生实验无法获得的数据，在某些情况下甚至可以代替实验。如果用数值模拟代替实验，可以节省大量的时间和金钱。研究的目标是开发技术来解决凝固问题，目前超出了数值模拟的范围。为了实现这一目标，研究人员将结合现有的最佳数值方法，并将其扩展到解决更复杂的问题。

Solidification processes are ubiquitous in modern technology. They are important whenever a substance changes from a liquid or gas to a solid, for example when ice melts or freezes, when silicon or gallium arsenide crystals are grown for use in semiconductor devices or silver halide crystals grown for film production, when Alaskan soil freezing patterns are altered by an oil pipeline, or when zinc dendrites pierce the walls of a lead- zinc battery. Computer simulation of solidification processes, the subject of this activity, serves two purposes. When the fundamental physics is under investigation, the theoretical predictions of any proposed model must be produced and compared with other models and with experiment. Solidification is sufficiently complex that this must be done by careful numerical simulation; exact solutions almost never exist. Once the fundamental physics is well understood, numerical calculations can produce data inaccessible to experiment and in some situations can even substitute for experiment. Considerable savings in time and money can be realized if numerical simulation can be substituted for experiments. The goal of the research is to develop technology to solve solidification problems which are presently beyond the reach of numerical simulation. To achieve this goal, the investigators will combine the best numerical methods available and extend them to solve more complex problems.